Heat a gas grill to medium or prepare a medium charcoal fire.
Put the asparagus on a rimmed baking sheet, drizzle with 2 Tbs. of the oil, and season with 1/2 tsp. of the salt and a few generous grinds of black pepper. Turn to coat. Grill the asparagus (covered on a gas grill) until they have nice grill marks, about 4 minutes. Turn and continue cooking until tender and browned, about 4 more minutes; transfer to a large platter. Reduce the heat on the gas grill to medium low or let the charcoal burn down a bit.
On a rimmed baking sheet, coat the onions with 2 Tbs. of the oil, the remaining 1/2 tsp. salt, and several grinds of pepper. Grill, covered, until tender and browned, 8 to 10 minutes per side. Return the onions to the baking sheet.
In a small bowl, whisk together the remaining 1/4 cup olive oil, the vinegar, and thyme. Toss the asparagus with about half the vinaigrette and then arrange neatly on the platter. Scatter the onions over the asparagus and drizzle with the remaining vinaigrette. Sprinkle with the blue cheese, figs, and pine nuts, and serve; this can sit for up to 1 hour at room temperature.